A Simple Method for Getting Standard Error on the Ratiometric Calcium Estimator
Résumé
1. Abstract The ratiometric fluorescent calcium indicator Fura-2 plays a fundamental role in the investigation of cellular calcium dynamics. Despite of its widespread use in the last 30 years, only one publication [2] proposed a way of obtaining confidence intervals on fitted calcium dynamic model parameters from single ’calcium transients’. Shortcomings of this approach are its requirement for a ’3 wavelengths’ protocol (excitation at 340 and 380 nm as usual plus at 360 nm, the isosbectic point) as well as the need for an autofluorence / background fluorescence model at each wavelength. We propose here a simpler method that eliminates both shortcommings: a precise estimation of the standard errors of the raw data is obtained first, the standard error of the ratiometric calcium estimator (a function of the raw data values) is derived using both the propagation of uncertainty and a Monte-Carlo method. Once meaningful standard errors for calcium estimates are available, standard errors on fitted model parameters follow directly from the use of nonlinear least-squares optimization algorithms. 2. Graphical abstract Figure 1: How to get error bars on the ratiometric calcium estimator? The figure is to be read clockwise from the bottom right corner. The two measurements areas (region of interest, ROI, on the cell body and background measurement region, BMR, outside of the cell) are displayed on the frame corresponding to one actual experiment. Two measurements, one following an excitation at 340 nm and the other following an excitation at 380 nm are performed (at each ’time point’) from each region. The result is a set of four measures: adu340 (from the ROI), adu340B (from the BMR), adu380 and adu380B. These measurements are modeled as realizations of Gaussian random variables . The fact that the measurements as well as the subsequent quantities derived from them are random variable realization is conveyed throughout the figure by the use of Gaussian probability densities. The densities from the MRB are ’tighter’ because there are much more pixels in the MRB than in the ROI (the standard deviations of the densities shown on this figure have been enlarged for clarity, but their relative size has been preserved, the horizontal axis in black always starts at 0). The key result of the paper is that the standard deviation of the four Gaussian densities corresponding to the raw data (bottom of the figure) can be reliably estimated from the data alone, , where V is the product of the CCD chip gain squared by the number of pixels in the ROI by the CCD chip readout variance. The algebric operations leading to the estimator (top right) are explicitely displayed. The paper explains how to compute the standard deviation of the derived distributions obtained at each step of the calcium concentration estimation. Method name Standard error for the ratiometric calcium estimator
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